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• W2950341978 abstract "The objective of this paper is to develop a general algebraic theory of matrix algebra, extending [11]. Our main results are as follows: * The tropical determinant (i.e., permanent) is multiplicative when all the determinants involved are tangible. * There exists an adjoint matrix $adj{A}$ such that the matrix $A adj{A}$ behaves much like the identity matrix (times $|A|$). * Every matrix $A$ is a root of its Hamilton-Cayley polynomial $f_A$. If these roots are distinct, then $A$ is conjugate (in a certain sense) to a diagonal matrix. * The tropical determinant of a matrix $A$ is a ghost iff the rows of $A$ are tropically dependent, iff the columns of $A$ are tropically dependent. * Every root of $f_A$ is a supertropical eigenvalue of $A$ (appropriately defined), and has a tangible eigenvector." @default.
• W2950341978 created "2019-06-27" @default.
• W2950341978 creator A5020188998 @default.
• W2950341978 creator A5033661144 @default.
• W2950341978 date "2008-06-06" @default.
• W2950341978 modified "2023-09-25" @default.
• W2950341978 title "Supertropical matrix algebra" @default.
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